Ladder and number operators of the quantum harmonic oscillator

What are the ladder and number operators associated with the quantum harmonic oscillator?

📚 Ladder operators allow us to increase or decrease the energy of a quantum harmonic oscillator by a discrete amount, called a quantum of energy. The number operator allows us to count the number of energy quanta in the system. In this video, we derive a long list of properties of ladder and number operators that will prove extremely useful in our study of the quantum harmonic oscillator.

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⏮️ BACKGROUND
Hermitian operators: https://youtu.be/XIgDUfyrLAY
Harmonic oscillator: https://youtu.be/OdizRUe84bg

⏭️ WHAT NEXT?
Harmonic oscillator eigenvalues: https://youtu.be/GkUXscdLQQ0
Harmonic oscillator eigenstates: https://youtu.be/0o-LoJRtxDc
Ladder operators in angular momentum: https://youtu.be/yGvfqRfw1BE

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Director and writer: BM
Producer and designer: MC

Видео Ladder and number operators of the quantum harmonic oscillator канала Professor M does Science